The incidence matrix of a general block design is N=(beginsmallmatrix1&1&11&0&00&1&00&1&1endsmallmatrix). Hence the number of estimable orthogonal block contrasts is:

Q169Section III (Statistics)169 of 190

Counting estimable orthogonal contrasts via the rank of the block design's information matrix

The incidence matrix of a general block design is $N=\left(\begin{smallmatrix}1&1&1\\1&0&0\\0&1&0\\0&1&1\end{smallmatrix}\right)$ . Hence the number of estimable orthogonal block contrasts is:

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